Which of the following pairs of linear equations are consistent/

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 Multiple Choice QuestionsShort Answer Type

11. On comparing the ratios straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 find out whether the following pair of linear equations are consistent, or inconsistent.

space space space space space space 3 over 2 straight x plus 5 over 3 straight y equals 7 semicolon space 9 straight x minus 10 straight y equals 14
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12. On comparing the ratios straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 find out whether the following pair of linear equations are consistent, or inconsistent.

5x-3y=11 ; -10x + 6y = -22

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13. On comparing the ratios straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 find out whether the following pair of linear equations are consistent, or inconsistent.

4 over 3 straight x space plus space 2 straight y equals 8 space semicolon space 2 straight x space plus space 3 straight y equals space 12

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 Multiple Choice QuestionsLong Answer Type

14. Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

x + y = 5, 2x + 2y = 10
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15. Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

x – y = 8, 3x – 3y = 16


x - y = 8

⇒    y = x - 8

Thus we have following table

x - y = 8
⇒    y = x - 8
Thus we have following tableThus, we ha

3 straight x minus 3 straight y equals 16
rightwards double arrow space space space straight y space space equals space fraction numerator 3 straight x minus 16 over denominator 3 end fraction
Thus, we have following table :


x - y = 8
⇒    y = x - 8
Thus we have following tableThus, we ha

When we plot the graph of the equations. We find the both the lines never meet.

Hence, lines are parallel and equation has no solution.


x - y = 8
⇒    y = x - 8
Thus we have following tableThus, we ha

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16. Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

2x + y – 6 = 0,      4x – 2y – 4 = 0
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17. Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

2x – 2y – 2 = 0, 4x – 4y – 5 = 0
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18.

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

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 Multiple Choice QuestionsShort Answer Type

19.

Given the linear equations 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representing of the pair so formed is :

(i) intersecting lines

(ii) parallel lines

(iii) coincident lines.

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20.

Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

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